Weak Convergence of Generalized $U$-Statistics

Weak Convergence of Generalized U - Statistics

Weak and strong convergence theorems for a finite family of generalized asymptotically quasinonexpansive nonself-mappings

In this paper, we introduce and study a new iterative scheme toapproximate a common xed point for a nite family of generalized asymptoticallyquasi-nonexpansive nonself-mappings in Banach spaces. Several strong and weakconvergence theorems of the proposed iteration are established. The main resultsobtained in this paper generalize and rene some known results in the currentliterature.

Convergence of U-statistics for interacting particle systems

The convergence of U -statistics has been intensively studied for estimators based on families of i.i.d. random variables and variants of them. In most cases, the independence assumption is crucial [Lee90, dlPG99]. When dealing with Feynman-Kac and other interacting particle systems of Monte Carlo type, one faces a new type of problem. Namely, in a sample of N particles obtained through the cor...

Asymptotics for the Moment Convergence of U-Statistics in LIL

A Remark on Convergence in Distribution of U-statistics

It is proved that, for h measurable and symmetric in its arguments and Xi i.i.d., if the sequence {n−m2 ∑ i1,...,im≤n ij 6=ik if j 6=k h(Xi1 ,...,Xim )}n=1, is stochastically bounded, then Eh2<∞ and Eh(X1,x2,...,xm)=0 a.s.